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Robust stability for stochastic Hopfield neural networks with time delays. (English) Zbl 1122.34065
The Hopfield neural network is described by a stochastic delay differential equation of the form $dx(t)=(-Ax(t)+W l(x(t-h)))dt+(Cx(t)+Dx(t-h))dw(t).$ Here $$A,W,C,D$$ are matrices with certain properties, $$l$$ is a Lipschitz continuous neuron activity function and $$w$$ is a Brownian motion. It is shown that certain explicit matrix inequalities imply that the equilibrium solution is robustly, globally, asymptotically stable in the mean-square sense.

##### MSC:
 34K50 Stochastic functional-differential equations 34K20 Stability theory of functional-differential equations 93D09 Robust stability 92B20 Neural networks for/in biological studies, artificial life and related topics
LMI toolbox
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